# 5.1 | Antiderivatives and Indefinite Integration

Definition of Antiderivative
A function $$F$$ is an antiderivative of $$f$$ on an interval $$I$$ when $$F'(x) = f(x)$$ for all $$x$$ in $$I$$.
Representation of Antiderivatives
If $$F$$ is an antiderivative of $$f$$ on an interval $$I$$, then $$G$$ is an antiderivative of $$f$$ on the interval $$I$$ if and only if $$G$$ is of the form $$G(x) = F(x) +C$$, for all $$x$$ in $$I$$ where $$C$$ is a constant.